Book Cover
Book
Author Pach, János.

Title Combinatorial geometry and its algorithmic applications : the Alcalá lectures / János Pach, Micha Sharir
Published Providence, R.I. : American Mathematical Society, 2009

Copies

Location Call no. Vol. Availability
 MELB  516.13 Pac/Cga  AVAILABLE
Description viii, 235 pages : illustrations ; 27 cm
Series Mathematical surveys and monographs ; v. 152
Mathematical surveys and monographs ; no. 152
Contents Machine derived contents note: Contents -- Preface and Apology vii -- Chapter 1. Sylvester{Gallai Problem: -- The Beginnings of Combinatorial Geometry 1 -- 1. James Joseph Sylvester and the Beginnings 1 -- 2. Connecting Lines and Directions 3 -- 3. Directions in Space vs. Points in the Plane 6 -- 4. Proof of the Generalized Ungar Theorem 7 -- 5. Colored Versions of the Sylvester{Gallai Theorem 10 -- Chapter 2. Arrangements of Surfaces: -- Evolution of the Basic Theory 13 -- 1. Introduction 13 -- 2. Preliminaries 16 -- 3. Lower Envelopes 20 -- 4. Single Cells 27 -- 5. Zones 29 -- 6. Levels 32 -- 7. Many Cells and Related Problems 37 -- 8. Generalized Voronoi Diagrams 40 -- 9. Union of Geometric Objects 42 -- 10. Decomposition of Arrangements 49 -- 11. Representation of Arrangements 54 -- 12. Computing Arrangements 56 -- 13. Computing Substructures in Arrangements 58 -- 14. Applications 63 -- 15. Conclusions 70 -- Chapter 3. Davenport{Schinzel Sequences: -- The Inverse Ackermann Function in Geometry 73 -- 1. Introduction 73 -- 2. Davenport{Schinzel Sequences and Lower Envelopes 74 -- 3. Simple Bounds and Variants 79 -- 4. Sharp Upper Bounds on ıs(n) 81 -- 5. Lower Bounds on ıs(n) 86 -- 6. Davenport{Schinzel Sequences and Arrangements 89 -- Chapter 4. Incidences and Their Relatives: -- From Szemerœedi and Trotter to Cutting Lenses 99 -- 2. Lower Bounds 102 -- 3. Upper Bounds for Incidences via the Partition Technique 104 -- 4. Incidences via Crossing Numbers
Summary "Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s
The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks. "Combinatorial Geometry and Its Algorithmic Applications" is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography."--BOOK JACKET
Bibliography Includes bibliographical references (pages 197-226) and index
Notes Also available online (Table of contents)
Subject Combinatorial geometry.
Algorithms.
Author Sharir, Micha.
LC no. 2008038876
ISBN 9780821846919 alkaline paper
0821846914 alkaline paper